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Search results for: FLOW EQUATIONS
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Inverse Integration of the Open Channel Flow Equations
PublicationW artykule przedstawiono metodę obliczeń umożliwiającą całkowanie równań przepływu nieustalonego w kanałach otwartych (równań de Saint Venanta) wstecz. Dyskutowano także przydatność równania retencji w zagadnieniu sterowania przepływem.
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Inverse Flood Routing Using Simplified Flow Equations
PublicationThe paper considers the problem of inverse flood routing in reservoir operation strategy. The aim of the work is to investigate the possibility of determining the hydrograph at the upstream end based on the hydrograph required at the downstream end using simplified open channel flow models. To accomplish this, the linear kinematic wave equation, the diffusive wave equation and the linear Muskingum equation are considered. To achieve...
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Numerical aspects of improvement of the unsteady pipe flow equations
PublicationW pracy dokonano analizy zaproponowanych w ostatnich latach metod opisu oporów ruchu w przepływie nieustalonym w przewodach pod ciśnieniem. Wykazano,że modyfikacja współczynnika oporów liniowych nie może zapewnić pozytywnych efektów oraz ,że poprawa wyników wykazywana przez autorów modyfikacji wynika z błędu dyfuzji numerycznej generowanej przez metodę rozwiązania.
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PROPERTIES OF ONE DIMENSIONAL OPEN-CHANNEL STEADY FLOW EQUATIONS
PublicationIn this paper properties of discrete forms of one dimensional steady gradually varied flow equations are discussed. Such forms of flow equations are obtained as a result of approximation of their differential forms, which is required to solve them numerically. For such purpose explicit or implicit numerical approximation schemes for ordinary differential equations can be applied. It turns out that dependently on the chosen approximation...
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Balance errors generated by numerical diffusion in the solution of non-linear open channel flow equations
PublicationThe paper concerns the untypical aspect of application of the dissipative numerical methods to solve nonlinear hyperbolic partial differential equations used in open channel hydraulics. It is shown that in some cases the numerical diffusion generated by the applied method of solution produces not only inaccurate solution but as well as a balance error. This error may occur even for an equation written in the conservative form not...
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Alternative Approach to Convolution Term of Viscoelasticity in Equations of Unsteady Pipe Flow
PublicationIn the paper the selected aspects concerning description of viscoelastic behavior of pipe walls during unsteady flow are analyzed. The alternative convolution expression of the viscoelastic term is presented and compared with the corresponding term referring to unsteady friction. Both approaches indicate similarities in the forms of impulse response functions and the parameter properties. The flow memory was introduced into convolution...
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Numerical analysis of open channel steady gradually varied flow using the simplified saint-venant equations
PublicationFor one-dimensional open-channel flow modeling, the energy equation is usually used. There exist numerous approaches using the energy equation for open-channel flow computations, which resulted in the development of several very efficient methods for solving this problem applied to channel networks. However, the dynamic equation can be used for this purpose as well. This paper introduces a method for solving a system of non-linear...
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Method to solve the non-linear systems of equations for steady gradually varied flow in open channel network.
PublicationW artykule omówiono rozwiązanie systemu równań nieliniowych opisujacych przepływ ustalony wolnozmienny w sieci kanałów otwartych. Niewiadomymi są glębokości w poszczególnych przekrojach oraz natężenia przepływów w poszczególnych gałęziach systemu. Układ musi być rozwiązywany iteracyjnie. Klasyczne metody Picarda i Newtona mogą okazać się nieskuteczne ze względu na oscylacje rozwiązania w kolejnych iteracjach i związany z tym brak...
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Two-dimensional vertical Reynolds-averaged naviers-stokes equations versus one-dimensional Saint-Venant model for rapidly varied open channel water flow modelling
PublicationPrzedstawiono dwa modele przepływu wody ze swobodną powierzchnią -płaski pionowy model Reynoldsa i model de Saint-Venanta.Do rozwiązania równań pierwszego modelu zastosowano schemat SIMPLE oraz wykorzystano metodę cząstek znaczonych MAC do wyznaczania swobodnej powierzchni wody. Równania Saint-Venanta rozwiązano metodą objętości skończonych. Obydwa modele zastosowano do symulacj zjawiska typu katastrofa zapory. Porównano wyniki...
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Equations of tribological parameters for liquid flow in boundary layer on the tissue surface in bioreactor = Wyznaczanie parametrów tribologicznych dla przepływu cieczy w warstwie granicznej na powierzchni tkanki w bioreaktorze
PublicationW niniejszej pracy przedstawiony został problem tribologiczny wynikający z przepływu nieustalonego odżywczej cieczy lepkiej w cienkiej warstwie przyściennej w bezpośrednim kontakcie z zewnętrzną powierzchnią warstwy wierzchniej wzrastających komórek (chondrocytów) w trakcie procesu ich hodowli w bioreaktorze. Efektem rozważań będą wartości sił tarcia powstające na powierzchni wzrastającej tkanki. Najnowsze badania wykazały lepszą...
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Nonlinear Interaction of Modes in a Planar Flow of a Gas with Viscous and Thermal Attenuation
PublicationThe nonlinear interaction of wave and non-wave modes in a gas planar flow are considered. Attention is mainly paid to the case when one sound mode is dominant and excites the counter-propagating sound mode and the entropy mode. The modes are determined by links between perturbations of pressure, density, and fluid velocity. This definition follows from the linear conservation equations in the differential form and thermodynamic...
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Analytical Steady-State Model of the Pipeline Flow Process
PublicationThe paper addresses the issue of modeling the flow process in transmission pipelines. A base model used for numerical simulation is introduced. Under certain assumptions concerning steady state analysis, the differential equations describing the process are solved analytically for two cases: zero and nonzero inclination angle α. These equations describe a constant flow rate and a corresponding distribution of the pressure along...
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Acoustic Heating Produced in the Thermoviscous Flow of a Shear-Thinning Fluid
PublicationThis study is devoted to the instantaneous acoustic heating of a shear-thinningfluid. Apparent viscosity of a shear-thinning fluid depends on the shear rate. Thatfeature distinguishes it from a viscous Newtonian fluid. The special linear combi-nation of conservation equations in the differential form makes it possible to derivedynamic equations governing both the sound and non-wave entropy mode inducedin the field of sound. These...
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A Comparison of Simplified Two-dimensional Flow Models Exemplified by Water Flow in a Cavern
PublicationThe paper shows the results of a comparison of simplified models describing a two-dimensional water flow in the example of a water flow through a straight channel sector with a cavern. The following models were tested: the two-dimensional potential flow model, the Stokes model and the Navier-Stokes model. In order to solve the first two, the boundary element method was employed, whereas to solve the Navier-Stokes equations, the...
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Reduction of Computational Complexity in Simulations of the Flow Process in Transmission Pipelines
PublicationThe paper addresses the problem of computational efficiency of the pipe-flow model used in leak detection and identification systems. Analysis of the model brings attention to its specific structure, where all matrices are sparse. With certain rearrangements, the model can be reduced to a set of equations with tridiagonal matrices. Such equations can be solved using the Thomas algorithm. This method provides almost the same values...
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Application of the Boundary Element Method for the Simulation of Two-dimensional Viscous Incompressible Flow
PublicationThe paper presents the application of an indirect variant of the boundary element method (BEM) to solve the two-dimensional steady flow of a Stokes liquid. In the BEM, a system of differential equations is transformed into integral equations. Thi smakes it possible to limit discretization to the border of the solution. Numerical discretization of the computational domain was performed with linear boundary elements, for which a...
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Determination of dryout localization using a five-equation model of annular flow for boiling in minichannels
PublicationDetailed studies have suggested that the critical heat flux in the form of dryout in minichannels occurs when the combined effects of entrainment, deposition, and evaporation of the film make the film flow rate go gradually and smoothly to zero. Most approaches so far used the mass balance equation for the liquid film with appropriate formulations for the rate of deposition and entrainment respectively. It must be acknowledged...
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Balance errors in numerical solutions of shallow water equations
PublicationThe analysis of the conservative properties of the shallow water equations is presented in the paper. The work focuses on the consistency of numerical solution of these equations with the conservation laws of mass and momentum. The investigations involve two different conservative forms which are solved by an implicit box scheme. The theoretical analysis supported by numerical experiments is carried out for rectangular channel...
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Acoustic heating produced in the thermoviscous flow of a Bingham plastic
PublicationThis study is devoted to the instantaneous acoustic heating of a Bingham plastic. The model of the Bingham plastic's viscous stress tensor includes the yield stress along with the shear viscosity, which differentiates a Bingham plastic from a viscous Newtonian fluid. A special linear combination of the conservation equations in differential form makes it possible to reduce all acoustic terms in the linear part of of the final equation...
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Acoustic heating produced in the thermoviscous flow of a bingham plastic
PublicationThis study is devoted to the instantaneous acoustic heating of a Bingham plastic. The model of the Bingham plastic's viscous stress tensor includes the yield stress along with the shear viscosity, which differentiates a Bingham plastic from a viscous Newtonian fluid. A special linear combination of the conservation equations in differential form makes it possible to reduce all acoustic terms in the linear part of of the final equation...
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ADAPTIVE METHOD FOR THE SOLUTION OF 1D AND 2D ADVECTION-DIFFUSION EQUATIONS USED IN ENVIRONMENTAL ENGINEERING
PublicationThe paper concerns the numerical solution of one-dimensional (1D) and two-dimensional (2D) advection-diffusion equations. For the numerical solution of the 1D advection-diffusion equation a method, originally proposed for solution of the 1D pure advection equation, has been developed. A modified equation analysis carried out for the proposed method allowed increasing of the resulting solution accuracy and consequently, to reduce...
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DISTRIBUTION OF FLOWS IN A CHANNEL NETWORK UNDER STEADY FLOW CONDITIONS
PublicationThe article presents an algorithm for calculating the distribution of flow in a junction of open channel network under steady flow conditions. The article presents a simplified calculation algorithm used to estimate the distribution of flow in a network of channels under steady flow conditions. The presented algorithm is based on the continuity equation and a simplified energy equation. To describe the relationship between the...
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Lax-Wendroff and McCormack Schemes for Numerical Simulation of Unsteady Gradually and Rapidly Varied Open Channel Flow
PublicationTwo explicit schemes of the finite difference method are presented and analyzed in the paper. The applicability of the Lax-Wendroff and McCormack schemes for modeling unsteady rapidly and gradually varied open channel flow is investigated. For simulation of the transcritical flow the original and improved McCormack scheme is used. The schemes are used for numerical solution of one dimensional Saint-Venant equations describing free...
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Modular Approach for Modelling Warming Up Process in Water Installations with Flow-Regulating Elements
PublicationThe paper presents a new method for modelling the warming up process of a water system with elements regulating the flow in a stochastic manner. The paper presents the basic equations describing the work of typical elements which the water installation is composed of. In the proposed method, a new computational algorithm was used in the form of an iterative procedure enabling the use of boundary conditions that can be stochastically...
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Vortex flow caused by periodic and aperiodic sound in a relaxing maxwell fluid
PublicationThis paper concerns the description of vortex flow generated by periodic and aperiodic sound in relaxing Maxwell fluid. The analysis is based on governing equation of vorticity mode, which is a result of decomposition of the hydrodynamic equations for fluid flow with relaxation and thermal conductivity into acoustical and non-acoustical parts. The equation governing vorticity mode uses only instantaneous, not averaged over sound...
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Discrete-continuous optimisation of an axial flow blood pump
PublicationThis paper presents results of discrete-continuous optimisation of an axial flow blood pump. Evolution Strategies (ES) are used as a global optimisation method in order to localise the optimal solution in relatively short time. The whole optimisation process is fully automated. This also applies to geometry modelling. Numerical simulations of the flow inside the pump is performed by means of the Reynolds-Average Navier-Stokes...
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The Discrete-Continuous, Global Optimisation of an Axial Flow Blood Pump
PublicationThis paper presents the results of the discrete-continuous optimisation of an axial flow blood pump. Differential evolution (DE) is used as a global optimisation method in order to localise the optimal solution in a relatively short time. The whole optimisation process is fully automated. This also applies to geometry modelling. Numerical simulations of the flow inside the pump are performed by means of the Reynolds-Average Navier-Stokes...
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Approximate models and parameter analysis of the flow process in transmission pipelines
Publicationthe paper deals with the problem of early leak detection in transmission pipelines. First we present the derivation of state-space equations of the flow process in the pipelines. This description is then aggregated in order to obtain a principal model. Next, the problem of process model parameterization is addressed, taking into account the maximization of a model stability margin. The location of the maximum is determined using...
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A significance of multi slip condition for inclined MHD nano-fluid flow with non linear thermal radiations, Dufuor and Sorrot, and chemically reactive bio-convection effect
PublicationThe aim of this research is to discuss the significance of slip conditions for magnetized nanofluid flow with the impact of nonlinear thermal radiations, activation energy, inclined MHD, sorrot and dufour, and gyrotactic micro motile organisms over continuous stretching of a two-dimensional sheet. The governing equations emerge in the form of partial differential equations. Since the resultant governing differential equations...
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Numerical simulation of cold flow and combustion in a swirl stabilized combustor
PublicationA numerical simulation model was developed to investigate the cold flow and combustion using Ansys FLUENT 2021R1. The governing equations were solved using the pressure-based method, and pressure–velocity coupling was performed using the SIMPLE method. To model the turbulent process, the RSM model was used. Non-premixed model is chosen to solve the chemical kinetics between fuel and oxigen. Radiation heat transfer was calculated...
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Effects of subfilter velocity modelling on dispersed phase in LES of heated channel flow
PublicationA non-isothermal turbulent flow with the dispersed phase is modelled using the Large Eddy Simulation (LES) approach for fluid, one-way coupled with the equations of point-particle evolution. The channel is heated at both walls and isoflux boundary conditions are applied for fluid. Particle velocity and thermal statistics are computed. Of particular interest are the r.m.s. profiles and the probability density function of particle...
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Numerical Analysis of Steady Gradually Varied Flow in Open Channel Networks with Hydraulic Structures
PublicationIn this paper, a method for numerical analysis of steady gradually varied fl ow in channel networks with hydraulic structures is considered. For this purpose, a boundary problem for the system of ordinary differential equations consisting of energy equation and mass conservation equations is formulated. The boundary problem is solved using fi nite difference technique which leads to the system of non-linear algebraic equations....
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Modeling and simulation of blood flow under the influence of radioactive materials having slip with MHD and nonlinear mixed convection
PublicationRadioactive materials are widely in industry, nuclear plants and medical treatments. Scientists and workers in these fields are mostly exposed to such materials, and adverse effects on blood and temperature profiles are observed. In this regard, objective of the current study is to model and simulate blood based nanofluid with three very important radioactive materials, named as Uranium dioxide (UO2), Thorium dioxide (ThO2) and...
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Study of Slip Effects in Reverse Roll Coating Process Using Non-Isothermal Couple Stress Fluid
PublicationThe non-isothermal couple stress fluid inside a reverse roll coating geometry is considered. The slip condition is considered at the surfaces of the rolls. To develop the flow equations, the mathematical modelling is performed using conservation of momentum, mass, and energy. The LAT (lubrication approximation theory) is employed to simplify the equations. The closed form solution for velocity, temperature, and pressure gradient...
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Acoustic heating produced in the boundary layer
Publication: Instantaneous acoustic heating of a viscous fluid flow in a boundary layer is the subject of investigation. The governing equation of acoustic heating is derived by means of a special linear combination of conservation equations in the differential form, which reduces all acoustic terms in the linear part of the final equation but preserves terms belonging to the thermal mode. The procedure of decomposition is valid in a weakly...
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A finite element analysis of thermal energy inclination based on ternary hybrid nanoparticles influenced by induced magnetic field
PublicationThe use of hybrid nanoparticles to improve thermal processes is a key method that has implications for a variety of interventions utilized in many sectors. This paper aimed to look into the impacts of ternary nanoparticles on hyperbolic tangent materials to establish their thermal characteristics. Flow describing equations have been explored in the presence of heat production, non-Fourier heat flux, and an induced magnetic field....
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Analytical ‘Steady-State’-Based Derivation and Clarification of the Courant-Friedrichs-Lewy Condition for Pipe Flow
PublicationThis article addresses the problem of choosing the optimal discretization grid for emulating fluid flow through a pipeline. The aggregated basic flow model is linearized near the operating point obtained from the steady state analytic solution of the differential equations under consideration. Based on this model, the relationship between the Courant number (μ) and the stability margin is examined. The numerically set coefficient...
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The description of non-linear interactions of wave and non-wave modes in a non-adiabatic plasma flow
PublicationThe method of derivation of non-linear equations for interacting modes is explained and applied to a plasma's flow affected by a magnetic field. It is based on the linear projecting of the total perturbation field into specific variations of variables in individual modes of a flow. The method may be applied in many examples of fluid flows with different mechanisms of non-adiabaticity. It is of special importance in complex flows...
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Coupled Urban Areas Inundation Model with Interaction Between Storm Water System and Surface Flow - Case Study of Sea Level Impact on Seaside Areas Flooding
PublicationInundations are becoming more frequent than ever. What is connected with increasing area of impervious surface in cities. This makes predicting urban flooding and its scale especially important. At the seaside we observe additional conditions such as sea level that makes accurate numerical modelling of issue even harder. With complex approach to the matter which is simultaneous calculation of storm water conduit flow and overland...
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An Experimental and Numerical Analysis of Water Hammer Phenomenon in Slurries
PublicationThe analysis of slurry transportation in pressure pipelines is important both from practical and theoretical point of view. Due to the nature of the medium, the number of problems arising in the course of design, operation, measurements and mathematical modeling is much higher compared to the cases where the flowing liquid is homogeneous. The equations describing the flow are more complex, and higher number of the parameters is...
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Magnetoacoustic heating in a quasi-isentropic magnetic gas
PublicationThe nonlinear heating of a plasma which associates with the transfer of energy of magnetoacoustic waves into that of the entropy mode, is analytically studied. A plasma is uniform and motionless at equilibrium. Perturbations in a plasma are described by a system of ideal magnetohydrodynamic equations. The equilibrium straight magnetic strength and the wave vector form a constant angle which varies from 0 to π/2. There exist four...
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Efficiency of acoustic heating produced in the thermoviscous flow of a fluid with relaxation
PublicationInstantaneous acoustic heating of a fluid with thermodynamic relaxation is the subject of investigation. Among others, viscoelastic biological media described by the Maxwell model of the viscous stress tensor, belong to this type of fluid. The governing equation of acoustic heating is derived by means of the special linear combination of conservation equations in differential form, allowing the reduction of all acoustic terms in...
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Modeling of medium flow processes in transportation pipelines - the synthesis of their state-space models and the analysis of the mathematical properties of the models for leak detection purposes
PublicationThe dissertation concerns the issue of modeling the pipeline flow process under incompressible and isothermal conditions, with a target application to the leak detection and isolation systems. First, an introduction to the model-based process diagnostics is provided, where its basic terminology, tools, and methods are described. In the following chapter, a review of the state of the art in the field of leak detection and isolation...
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Numeryczna analiza hydrauliki toru kajakarstwa górskiego w Drzewicy
PublicationW artykule zaproponowano wykorzystanie do analizy hydrodynamiki toru kajakarstwa górskiego symulacji numerycznej, wykorzystującej dwuwymiarowe równania ruchu wody w warunkach przepływu szybkozmiennego. Rozwiązanie równań hydrodynamiki wykonano samodzielnie z zastosowaniem metody objętości skończonych. Jako przykład zastosowania zaproponowanej metody przedstawiono analizę przepływu wzdłuż istniejącego, poddanego modernizacji toru...
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Simulations of flows in the coastal zone of the Baltic Sea
Open Research DataThe study area is located in the Southern Baltic, within Polish Marine Areas, adjacent to the coastline in the vicinity of Lubiatowo village, where The Coastal Research Station (CRS) – a field laboratory of the Institute of Hydro-Engineering of the Polish Academy of Sciences (IBW PAN) –is situated. The numerical reconstruction of the coastal flow was...
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Numerical Modelling of Forced Convection of Nanofluids in Smooth, Round Tubes: A Review
PublicationA comprehensive review of published works dealing with numerical modelling of forced convection heat transfer and hydrodynamics of nanofluids is presented. Due to the extensive literature, the review is limited to straight, smooth, circular tubes, as this is the basic geometry in shell-and-tube exchangers. Works on numerical modelling of forced convection in tubes are presented chronologically in the first part of the article....
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One-Dimensional Modeling of Flows in Open Channels
PublicationIn this chapter, modeling of the unsteady open channel flow using one-dimensional approach is considered. As this question belongs to the well-known and standard problems of open channel hydraulic engineering, comprehensively presented and described in many books and publications, our attention is focused on some selected aspects only. As far as the numerical solution of the governing equations is considered, one can find out that...
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New hybrid quadrature schemes for weakly singular kernels applied to isogeometric boundary elements for 3D Stokes flow
PublicationThis work proposes four novel hybrid quadrature schemes for the efficient and accurate evaluation of weakly singular boundary integrals (1/r kernel) on arbitrary smooth surfaces. Such integrals appear in boundary element analysis for several partial differential equations including the Stokes equation for viscous flow and the Helmholtz equation for acoustics. The proposed quadrature schemes apply a Duffy transform-based quadrature...
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Discussion of “Development of an Accurate Time integration Technique for the Assessment of Q-Based versus h-Based Formulations of the Diffusion Wave Equation for Flow Routing” by K. Hasanvand, M.R. Hashemi and M.J. Abedini
PublicationThe discusser read the original with great interest. It seems, however, that some aspects of the original paper need additional comments. The authors of the original paper discuss the accuracy of a numerical solution of the diffusion wave equation formulated with respect to different state variables. The analysis focuses on nonlinear equations in the form of a single transport equation with the discharge Q (volumetric flow rate)...
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Fluid Mechanics and Hydraulics EE Msc sem. I r.a. 22/23
e-Learning CoursesBasic definitions. Physical properties of liquids. Forces acting on fluids. Hydrostatics - basic equations. Pressure on a flat and curved wall. Buoyancy. Archimedes' law. Balance of submerged bodies. The balance of floating bodies. Hydrodynamics. Hydrodynamic quantities. Continuity equation for the liquid stream. Bernoulli equation. Basic laws of hydrodynamics. Equation of mass behavior, preservation of the amount of motion, Bernoulli's...